Q. $\cos^{4}{\theta - \sin^{4}\theta}$ is equal to
A) $1 + 2\sin^{2}\left( \frac{\theta}{2} \right)$
B) $2\cos^{2}{\theta - 1}$
C) $1 - 2\sin^{2}\left( \frac{\theta}{2} \right)$
D) $1 + 2\cos^{2}\theta$
Explanation
(b)
$\cos^{4}{\theta - \sin^{4}{\theta = \left( \cos^{2}{\theta - \sin^{2}\theta} \right)(\cos^{2}{\theta + \sin^{2}\theta})}}$
$= \cos{2\theta = 2\cos^{2}{\theta - 1}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.